Quick question-
I often move my fermenters around the house while my beer is fermenting. I take them to cooler spots of the house to keep them cool during active/primary fermentation and warmer parts of the house during aging/secondary fermentation. Is there any reason that disturbing/shaking the fermenting beer while carrying the fermenters around the house would have negative effects on the final product?

Your question depends on the stage of fermentation. If this is primary (very active) fermentation, disturbing the fermenting wort can be a good thing. It keeps the yeast in suspension and prevents stratification of the fermenting wort. Also the CO2 is very high in the fermenting vessel so the chance of oxidation is reduced. If it is later in fermentation (secondary fermentation), where CO2 generation is slow and yeast have been settled out, disturbing the wort would circulate hydrolyzed yeast products into the ferment as well as oxygen. Hydrolyzed yeast has a bitterness unlike hops and can produce an unpleasant taste.